Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students?(1 point)
Responses
200 students
200 students
124 students
124 students
50 students
50 students
250 studen
right answer please
To solve this problem using proportional relationships, we can set up the proportion:
number of band seats : number of choir seats = number of band students : number of choir students
Let's start by defining the number of band seats as "b" and the number of choir seats as "c". We are given that there are four times as many choir seats as band seats, so we can say that:
c = 4b
Now, we also know that the total number of students is 250. Thus, the number of band students + the number of choir students must equal 250:
b + c = 250
Since we know c = 4b, we can substitute it into the equation:
b + 4b = 250
Combining like terms, we get:
5b = 250
Now, we can solve for b by dividing both sides by 5:
b = 50
Therefore, there are 50 students who can choose band as their elective.
To solve this problem, we can set up a proportion between the number of seats in band and choir.
Let x be the number of seats in band.
Given that there are four times as many seats in choir, the number of seats in choir will be 4x.
The total number of students is 250. So, the sum of the number of students in band and choir is x + 4x = 5x.
We can set up the following proportion:
x / 5x = 250 / 250
Simplifying the proportions, we get:
1 / 5 = 1 / 1
Therefore, x = 1 * 5 = 5.
So, there are 5 seats in the band and 4 * 5 = 20 in the choir.
Therefore, the number of students who can choose band is 5.
To solve this mixture problem using proportional relationships, we need to set up a ratio between the number of seats in choir and band.
We are given that there are four times as many seats in choir as there are in band. Let's call the number of seats in the band "b" and the number of seats in the choir "c".
Since there are four times as many seats in choir as in band, we can write the ratio as:
c/b = 4/1
Now, we know that the total number of students is 250. So, the sum of the number of students in band and choir should be equal to 250.
b + c = 250
To solve this system of equations, we can use substitution.
From the first equation, we can rewrite it as:
c = 4b
Now substitute this value for "c" in the second equation:
b + 4b = 250
5b = 250
b = 50
So, there are 50 seats available in the band. Since the number of students in the band is equal to the number of seats, there can be 50 students who choose band as their elective.
Therefore, the correct answer is 50 students.